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    <title>variancef</title>
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    <div align="right">Last update : July 2000</div>
    <p>
      <b>variancef</b> -  standard deviation of the values of a  vector or matrix</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>s=variancef(x,fre)  </tt>
      </dd>
      <dd>
        <tt>s=variancef(x,fre,'r') or s=variancef(x,fre,1)  </tt>
      </dd>
      <dd>
        <tt>s=variancef(x,fre,'c') or s=variancef(x,fre,2)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>x</b>
        </tt>: real or complex vector or matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    This  function computes the variance  of the values of a
    vector  or matrix <tt>
        <b>x</b>
      </tt>,  each of  them counted with a
    frequency  signaled by  the corresponding values  of the
    integer vector or matrix <tt>
        <b>fre</b>
      </tt> with the same type of
    <tt>
        <b>x</b>
      </tt>.</p>
    <p>
    For a vector  or matrix <tt>
        <b>x</b>
      </tt>, <tt>
        <b>s=variancef(x,fre)</b>
      </tt> (or
    <tt>
        <b>s=variancef(x,fre,'*')</b>
      </tt>)  returns in scalar <tt>
        <b>s</b>
      </tt>  the
    variance of all  the   entries of <tt>
        <b>x</b>
      </tt>, each    value
    counted  with   the    multiplicity  indicated by    the
    corresponding value of <tt>
        <b>fre</b>
      </tt>.</p>
    <p>
      <tt>
        <b>s=variancef(x,fre,'r')</b>
      </tt>(or,                equivalently,
    <tt>
        <b>s=variancef(x,fre,1)</b>
      </tt>) returns in each  entry of the row
    vector  <tt>
        <b>s</b>
      </tt> of  type  1xsize(x,'c') the  variance of
    each column of  <tt>
        <b>x</b>
      </tt>,   each value counted  with  the
    multiplicity  indicated by  the  corresponding value  of
    <tt>
        <b>fre</b>
      </tt>.</p>
    <p>
      <tt>
        <b>s=variancef(x,fre,'c')</b>
      </tt>(or,                equivalently,
    <tt>
        <b>s=variancef(x,fre,2)</b>
      </tt>)  returns  in  each   entry of the
    column vector <tt>
        <b>s</b>
      </tt> of type size(x,'c') x1 the variance
    of  each row  of  <tt>
        <b>x</b>
      </tt>, each value  counted  with the
    multiplicity indicated  by  the  corresponding value  of
    <tt>
        <b>fre</b>
      </tt>.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>


x=[0.2113249 0.0002211 0.6653811;0.7560439 0.9546254 0.6283918]
fre=[1 2 3;3 4 3]
m=variancef(x,fre)
m=variancef(x,fre,'r')
m=variancef(x,fre,'c')

 
  </pre>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p> Carlos Klimann</p>
    <h3>
      <font color="blue">Bibliography</font>
    </h3>
    <p>
    Wonacott, T.H. &amp; Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley &amp; Sons, 1990.</p>
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